ltnme: Gibbs sampler for LTN-based mixed-effects model
In MaStatLab/LTN: Fit LTN model to microbiome count data

a wrapper for gibbs_crossgroup

ltnme(
  formula,
  data,
  test_baseline,
  niter,
  reffcov = 2,
  SEED = 1,
  save_alpha_only = F,
  gprior_m = 100,
  pnull = 0.5,
  lambda = 10
)

`formula`	a lme4 type formula where the first fixed effect is the group indicator
`data`	a phyloseq object
`test_baseline`	the group to be used as baseline in the linear model
`niter`	number of Gibbs iterations
`reffcov`	specification of the precision matrix of random effects. 1: diagonal, 2: sparse with graphical lasso prior
`SEED`	random seed for initializing the parameters
`save_alpha_only`	whether to only return posterior samples of alpha(A)
`gprior_m`	hyperparameter in prior of beta with default value 100
`pnull`	prior probability of the joint null hypothesis with default value 0.5
`lambda`	shrinkage parameter in the graphical lasso prior with default value 10